Question

Compressed APV with Nonconstant Growth Sheldon Corporation projects the following free cash flows (FCFs) and interest expenses for the next 3 years, after which FCF and interest expenses are expected to grow at a constant 5% rate. Sheldon's unlevered cost of equity is 11% its tax rate is 40%. Year 2 $30 $9 1 $20 $8 Free cash flow ($ millions) Interest expense ($ millions) 3 $40 $10 a. What is Sheldon's unlevered horizon value of operations at Year 3? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places. million b. What is the current unlevered value of operations? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places. million c. What is horizon value of the tax shield at Year 3? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places. million d. What is the current value of the tax shield? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places. million $ e. What is the current total value of the company? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places. million $

Answer 1

a.	Horizon value = (free cash flow Year 3 * (1+growth rate) / (WACC - growth rate)
		= 40 *(1+0.05)/(0.11-0.05)
		= 40*1.05/(0.06)
		=42/0.06
		=700 million
b.	Current Unlevered value of operations
		F	G	H	I
		Year	Free cash flow	FVIF @11%	Present value of Free cash flow
	14	1	20	1.110000	18.02
	15	2	30	1.232100	24.35
	16	3	40	1.367631	29.25
	17	Terminal value	700	1.367631	511.83
	18	Current value of operation			583.45
c.	Horizon value of tax shield 3rd year = (Interest expenses Year 3*tax rate * (1+growth rate) / (WACC - growth rate)
		= 10*0.4 *(1+0.05)/(0.11-0.05)
		= 4*1.05/(0.06)
		=4.2/0.06
		=70 million
d.	current value of tax shield
		F	G	H	I
		Year	Tax shield	FVIF @11%	Present value of Free cash flow
	31	1	3.2	1.110000	2.88
	32	2	3.6	1.232100	2.92
	33	3	4	1.367631	2.92
	34	Terminal value	70	1.367631	51.18
	35	Current value of Tax shield			59.91
e.	value of operation + value of tax shield
	= 583.45+59.91
	=643.36

formula:

Current Unlevered value of operations
	F	G	H	I
	Year	Free cash flow	FVIF @11%	Present value of Free cash flow
14	1	20	=(1+0.11)^F14	=G14/H14
15	2	30	=(1+0.11)^F15	=G15/H15
16	3	40	=(1+0.11)^F16	=G16/H16
17	Terminal value	700	=(1+0.11)^F16	=G17/H17
18	Current value of operation			=SUM(I14:I17)

	F	G	H	I
	Year	Tax shield	FVIF @11%	Present value of Free cash flow
31	1	=8*0.4	=(1+0.11)^F31	=G31/H31
32	2	=9*0.4	=(1+0.11)^F32	=G32/H32
33	3	=10*0.4	=(1+0.11)^F33	=G33/H33
34	Terminal value	70	=(1+0.11)^F33	=G34/H34
35	Current value of Tax shield			=SUM(I31:I34)